Petagons

**Rimas** · December 19th 2006, 03:47 PM

A diagnal of a polygon is a degment joining the two nonconecutive vertcies of the polygon.How many dianals does a regular octagon have?

**OReilly** · December 19th 2006, 03:50 PM

Originally Posted by Rimas

A diagonal of a polygon is a segment joining the two nonconsecutive vertcies of the polygon.How many dianals does a regular octagon have?

It has 20 diagonals.

Formula is:
$D_8 = \frac{{8(8 - 3)}}{2} = \frac{{40}}{2} = 20$

**AfterShock** · December 19th 2006, 03:51 PM

Originally Posted by Rimas

A diagnal of a polygon is a degment joining the two nonconecutive vertcies of the polygon.How many dianals does a regular octagon have?

We know that the octagon has exactly 8 vertices. We are then able to create 5 diagonals from a given vertex.

8*5 = 40; however, there are some repeats. Each diagonal is counted twice since there are 2 points to each diagonal. Thus, 40/2 = 20 is the number of diagonals in a regular octagon.

**OReilly** · December 19th 2006, 03:55 PM

General formula for counting number of diagonals for any polygon is:

$D_n = \frac{{n(n - 3)}}{2}$

where $n$ is number of sides.

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